A central idea behind the generalized fiducial method is the transfer of randomness from a known random quantity \(U\)  onto the parameter space \(\Theta \)  through an established Data Generating Algorithm (DGA), sometimes also called data generating equation or association equation. The DGA, denoted as \(\mathbf {y} = A(W,\theta )\) , must relate a known random quantity and parameter to the observed data \(\mathbf {y}\) . Under minor conditions on the DGA, [1]} perform the required transfer of randomness by defining the inverse of the DGA via the optimization problem
\(Q_\textbf {y}(W)=\text{argmin}_{\theta ^{\star } \in \mathbb {R}^d} {\Vert  \textbf {y} - A(W, \theta ^{\star } ) \Vert },\) 
